Mechanical properties of the esophageal wall

Raj K. Goyal, … , Aris Phillips, Howard M. Spiro

J Clin Invest. 1971;50(7):1456-1465. https://doi.org/10.1172/JCI106630.

Pressure-diameter curves of the esophagus were obtained to define its mechanicalproperties. The mucosal contribution to the strength of the esophagus was negligible untilthe outer diameter almost doubled, suggesting that small intraluminal pressures are held bythe muscle layer alone. For larger deformations mucosal contribution increased and atfailure the mucosa held over one-half of the failure pressure of the esophagus.

The paths followed during loading and unloading are different and exhibit hysteresis. Theyare influenced by the rate of pressure change, being more compliant for low rates ofpressure change. They are influenced by the history of loading, being different forsuccessive loading-unloading cycles. If enough loading-unloading cycles are repeated astable loop is reached, which does not change thereafter.

Both the mucosa and the whole esophagus show increasing stiffness with increasingpressure. This behavior can be represented by a simple exponential relationship. However,at rapid rates of pressure increases, the esophageal muscles produce sigmoid loadingcurves, which gradually become exponential when repeating loading.

Research Article

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Mechanical Properties of the Esophageal Wall

RAJ K. GoYAL, Pn;Ro BIANCANI, ARIs PPmuas, and HowARDM. SPIRo

From the Department of Internal Medicine, and the Department of Engineeringand Applied Science, Yale University, NewHaven, Connecticut 06510

A B S T R A C T Pressure-diameter curves of the esopha-gus were obtained to define its mechanical properties.The mucosal contribution to the strength of the esopha-gus was negligible until the outer diameter almostdoubled, suggesting that small intraluminal pressuresare held by the muscle layer alone. For larger deforma-tions mucosal contribution increased and at failure themucosa held over one-half of the failure pressure of theesophagus.

The paths followed during loading and unloading aredifferent and exhibit hysteresis. They are influenced bythe rate of pressure change, being more compliant forlow rates of pressure change. They are influenced by thehistory of loading, being different for successive loading-unloading cycles. If enough loading-unloading cyclesare repeated a stable loop is reached, which does notchange thereafter.

Both the mucosa and the whole esophagus show in-creasing stiffness with increasing pressure. This be-havior can be represented by a simple exponential re-lationship. However, at rapid rates of pressure increases,the esophageal muscles produce sigmoid loading curves,which gradually become exponential when repeatingloading.

INTRODUCTIONAn understanding of the mechanical characteristics ofthe materials constituting the walls of the gastrointestinaltract is necessary to evaluate its normal behavior aswell as conditions of failure, to understand the mechanicsof bolus transport, and to develop suitable biomaterialsfor replacement, when needed. Despite a renewed in-terest in biomechanics, as evidenced by recent studies onthe mechanical properties of blood vessels (1-3), lungs(4), muscles (5, 6), tendons (7, 8), skin (9), and manyother organs and tissues (10), little information isavailable on the mechanical properties of the gastro-

Dr. Goyal's present address is Department of Medicine,Baylor College of Medicine, Houston, Tex.

Received for publication 24 June 1970 and in revised form26 February 1971.

intestinal tract. The few studies on the pressure volumerelationship, as for example of colon (11), fall short indefining the mechanical behavior of this organ. This isbecause the volume of the balloon used in such studiesbears no constant relationship to the deformation orchanges in the diameter.

The purpose of this study was to define some of themechanical characteristics of the esophageal wall, usingthe rat as an experimental model.

METHODSDifferent experiments (over 200 in all) were performed onsmall groups of rats of the Sprague-Dawley strain, weigh-ing 200-300 g. The animals were anesthetized with etherinhalation and the esophagus was exposed after removingthe anterior wall of the thoracic cage, lungs, heart, andother mediastinal structures. The esophagus was tied at itslower end just above the diaphragm. A 1.5 mmouter diam-eter cannula was passed into the esophagus through themouth of the rat, and a ligature was placed around theupper end of the esophagus with the cannula passing throughit (Fig. 1). The thoracic cavity containing the esophaguswas perfused with constantly circulating Ringer's solutionat 370C ±1, which was oxygenated by bubbling through ita mixture of oxygen (95%) and carbon dioxide (5%).Intraluminal pressure was applied on the esophagus throughthe esophageal cannula by injecting fluid into it with aconstant infusion pump (Harvard Apparatus Co., Inc.,Millis, Mass., Model 944). The time between opening theanimal and the conclusion of the test was 20 min or less forall the experiments. The pressures were measured witheither a water manometer or a Sanborn pressure trans-ducer (Model 267 BC) and recorded on a Sanborn recorder(Hewlett-Packard Co., Waltham, Mass.) The outer diameterwas measured in the middle part of the esophagus with ameasuring microscope (Model 15, Bausch & Lomb Inc.,Rochester, N. Y.) which was graduated in 1/20 mm in-tervals and produced a magnification of 20. In some studiesmultiple photographs of the esophagus along with a measur-ing scale were taken, and the outer diameter of the esopha-gus was measured by projecting the slide and the scalereference on a large screen. This technique gave good agree-ment with the direct visual measurement of the outer diam-eter of the resting esophagus.

In the experiments described here, the outer diameter ofthe esophagus was measured. Estimates of the musclethickness and the inner diameter of muscle layer, and theouter and inner diameters of the mucosal layer were ob-

1456 The Journal of Clinical Investigation Volume 50 1971

tained in six animals. After exposing the esophagus, wefixed it in formalin and made sections at three points atvarious levels. After staining the sections, we projectedthem on a screen, measured the inner and outer perimetersof the muscular and mucosal layers; from these findingscalculated the diameters. The mean (-SD) diameter was 1.62+0.15 mm, muscle layer thickness 0.22 +0.02 mm, and theinner diameter of the muscular layer was 1.17 ±0.26 mm.

The mean outer diameter of the mucosal layer was largerthan the inner diameter of the muscle layer in which it iscontained, and for this reason, the mucosa in resting statewas thrown into folds.

Change in the thickness of the muscle layer with thechange in the outer diameter of the muscle wall can becalculated. If we assume that the volume and length, andthus also the cross-sectional area of the muscle coat andthe mucosal layer remain unchanged, the thickness of themuscle coat will vary with the outer diameter as shown inFig. 2. These calculations will hold provided the length ofthe esophagus does not change with increasing load andincreasing diameter. This point was checked in anothergroup of six rats. With stepwise increase of pressure to amaximum pressure of 80 g/cm2 there was an 8% reductionin length. This change did not appreciably influence the cal-culated thickness of the wall and can therefore be ignored.The hypotheses that the cross-sectional area does not varyas the diameter changes and that shrinkage is caused byformalin fixation, were verified experimentally in six ani-mals by introducing probes of fixed diameters in the lumenand measuring the corresponding outer diameters. From thediameters, the cross-sectional area was calculated and itwas found that the area remains unchanged as the deforma-tion proceeds but the formalin fixation causes a 47% shrink-age of the cross-sectional area.

The histologic examination shows that the muscle wallof the esophagus in the rat is composed of striated muscle

FIGURE 1 Experimental apparatus.

Thickness, mmxlcr2

20'

.10

2 3 4 OD mm

FIGURE 2 Thickness of muscle layer as a function of theouter diameter. The mean thickness of the muscle layerof the esophagus at resting diameter was estimated (pointon the top of the curve) by making cross-sections of theorgan in six animals and the curve was constructed by cal-culation assuming that the cross-sectional area of the musclewall does not change during deformation.

fibers throughout the entire length of this organ. Internalto the muscle layer is the loose connective tissue of thesubmucosa, followed in order by the thin muscularis mucosa,the lamina propria, and the squamous epithelium.

The loose connective tissue between the mucosa and themuscle layer form a convenient line of cleavage so that themuscle layer can be separated from the mucosal layer andso that a "mucosal sac" without external muscle layercan be made. To do this, the outer part of the wall of theesophagus is gently held with fine forceps and by pullingon the forceps, the mucosal layer can be seen shiningthrough the stretched muscle layer. A fine needle is theninserted between the mucosal sac and the muscle layer andsome saline is injected so that the mucosa, along with afew fibers of muscularis mucosa are separated from themuscle layer. The muscle layer is then easily dissected fromthe mucosal sac, with care being taken to avoid injury tothe sac. Histologic examination of these "mucosal sacs"shows complete absence of external muscle layer. The mus-cularis mucosa which is only a few fibers thick, remainsattached to the outer wall of the "mucosal sac."

Viability studies. In our preparation, the blood supplyto the esophagus was, of necessity, severed. The organ waskept viable by perfusing its outside with oxygenated Ringerat 37°C. Such a technique is adequate only for thin-walledorgans.

The viability of the preparation was tested; with a probeof 1.63 mmin diameter introduced into the esophagus, anelectrical stimulus was applied with a square wave (voltage,10 v; frequency, 30/sec; duration, 1 msec). The esophagealmuscle contracted to produce a mean pressure of 60 +22g/cm2.

After this, the esophagus was perfused with oxygenatedRinger as during the experiments and also an intraluminalload of P = 80 g/cm2 was applied for 15 min. Electrical ex-citation of the esophagus at the end of this period generateda pressure of P = 62 +25 g/cm2. A further load was appliedto the esophagus for another 15 min. At the end of this

Mechanical Properties of the Esophageal Wall 1457

Fe g/cm2

.160

loCo loading C) 'VIxcvunloading /RPC =5.

-I? !I I

80 RPC=06660 /

3 ~,P (B)

/ step I

.60 /

-40 ~ ~ ~ /

.20 /" ';/o 6 ,7r"

/ .--

3 4 Dmm

FIGURE 3 Mean loading and unloading curves for theesophagus at different rates of pressure change and at dif-ferent maximum pressures. (A) RPC= 0.66 (g/cm') /sec,Pmax = 80 g/cm' (10 experiments); (B) stepwise loading,Pmax = 80 g/cm2 (38 experiments); and (C) RPC= 5(g/cm2) /sec and Pm = 640 g/cm2 (10 experiments). Notethe shift in the curves due to different rates of loading.

period the esophageal muscle produced a pressure of 58±20 g/cm! on electrical stimulation. These studies indicatethat the preparation retains excellent viability for over 30min despite application of sustained load; all the experimentsreported were completed within 20 min. Christensen andLund (12) have shown that isolated esophagus in vitroresponds to distension as well as to electrical stimulation ina manner similar to that of the esophagus in intact animals.The viability of the mucosa was not separately tested, butbecause of the thin esophageal wall in rat we would assumethat the mucosa also remained viable during the experi-ments.

RESULTSPressure diameter relationship. In a group of 38 ani-

mals, stepwise pressure changes were applied up to amaximum pressure (P...) = 80 g/cm'. Small pressurechanges were applied at low pressures and large ones athigher pressures. After each pressure increment thediameter rapidly increased, and then the deformation ap-parently stopped. When the deformation had subsided,a new pressure increment was applied. A similar pro-cedure was followed during unloading. The curves ob-

tained showed a nonlinear pressure diameter relationship,the compliance descreasing with increasing loads.

Rate of pressure change and the pressure diameter re-lationship. When small increments of pressure at a con-stant rate of pressure change (RPC)' = 0.66 (g/cm')/sec were applied up to 80 g/cm, the loading curve wasquite different and was sigmoid in shape. The compli-ance increases at first and then starts to decrease as thepressure increases over 40 g/cm' (Fig. 3). This sig-moid behavior is entirely due to the muscle layer. Atsmall diameters the mucosa gives no contribution as itis thrown into longitudinal folds.

The loading curves showed a shift to the right withdecreasing rates of pressure increase so that the curvefor stepwise loading was to the extreme right (Fig. 3).This appears mostly to be due to time-related deforma-tion, or creep, occurring in the muscle wall at slow ratesof loading.

The unloading curves in all these experiments werequalitatively similar to each other. They were exponen-tial in character and exhibited no sigmoid behavior.All the unloading curves were different from the loadingcurves (Fig. 3).

Comparison of the pressure-diameter curves for mu-cosa alone and the esophagus. Loading and unloadingwere applied on the mucosal sac, with muscle removed,at a steady RPC= 0.66 (g/cm2)/sec. The behavior ofthe mucosa was very different from that of the esopha-gus at the same RPC, but was remarkably similar to thatof the esophagus under stepwise loading (Fig. 4); the

Pg/crm

(A) whoe (B) mucosaesopagusR R~66 (C)

0 ~~~RPC=066p 7'spaustepwise

60~~ ~~~~~ Qa~~~~ding-60

/ I :., K~0loadin

.20

'I)O

2 3 4 Dmm

FIGuRE 4 Mean loading and unloading curves for theesophagus at RPC= 0.66 (g/cm2)/sec (A); for the mucosaat RPC= 0.66 (g/cm2) /sec (B); and for the whole esopha-gus with stepwise loading (C). The behavior of the esoph-agus at RPC= 0.66 (g/cm2) /sec is different from the be-havior with stepwise loading. The curves of the esophaguswith stepwise loading are, however, very similar to thoseof the mucosa at RPC= (g/cm')/sec. (Each point is amean of 10 experiments.)

1458 R. K. Goyal, P. Biancani, A. Phillips, and H. M. Spiro

I/

4w %2

ng

only difference was noticed at low loads, when the mu-cosa undergoes a large deformation before starting tobear a load.

Rate-dependent deformation. The dependence of thediameter on the pressure and rate of pressure increase(RPI)' is shown in Fig. 5. In this figure the diameterduring the loading portions in the preceding experimentshas been plotted for various pressures and two rates ofpressure increase. The curves of constant pressureshow that for the same pressure the diameter increaseswith decreasing RPI and that the increase is moremarked for a very low RPI.

Dependence on the history of loading. To find theeffect of the previous loading history on the pressure-diameter relationship each esophagus was loaded andunloaded several times consecutively. In one experimentten different specimens were loaded five times by varyingthe pressure between 0 and 640 g/cm' at a constantRPC= 5 (g/cm2)/sec. With each loading-unloadingcycle the loading curves moved to the right (Fig. 6A),showing an increase in diameter. The increase was moremarked at lower loads and in the initial cycles. Theshift in the loading curve was most prominent betweenthe first and second cycle. The shift decreased progres-sively as more cycles occurred. A similar but muchsmaller shift was shown by the unloading curves (Fig.6 B). A sigmoid behavior was found in the first twocycles for RPC= 0.66 (g/cm')/sec, Pm.. = 80 g/cm'.After the first two cycles the sigmoid portion disappeared(Fig. 7).

The mucosa alone showed a nonsigmoid behavior(RPC = 0.66, Pm11 = 80 g/cm') except that the pathsfor loading and unloading remained completely un-changed after the second cycle (Fig. 8).

The area of hysteresis loop. The area of the hystere-sis loop is the area enclosed by a loading and the cor-responding unloading curve. The area of the hysteresisloop was different in the first cycles for different maxi-mal loads and different rates of pressure change. Thearea was smaller for stepwise loading than for a steadyRPC= 0.66 (g/cm2)/sec. Thus, the hysteresis loop isbigger for faster rates of pressure change and is re-duced as the RPCdecreases, and some time is availablefor the the deformation to take place. The loop was alsobigger for the whole esophagus than that for the mucosaalone, suggesting that it is the muscular layer whichcontributes most significantly to the area of the hysteresisloop (Fig. 4). On repeating loading-unloading cyclesthe shift of the loading curves is bigger than the shift ofthe unloading curves, which is always very small. As a

1 Abbreviations used in this paper: K, Fung's modulus; Liminimum length; L2, maximum length; Lo, a length com-prised between L1 and L2; RPC, constant rate of pressure;RPI, rate of pressure increase.

RPC ,g/cm sec

IP=o RATEDI

5I PP=

\

P=1 P4 BOOfP=0,1 _

2 3

)EPENDENCE

4 Dmm

FIGURE 5 Influence of the rate of pressure change on thediameter of the esophagus at a given pressure. Mean curvesgiving the dependence of the diameter on the RPCat variousconstant pressures (10-20-40-80 g/cm2) have been con-structed by plotting points from the loading curves of theesophagus at RPC= 5 (g/cm2) sec, (10 experiments),RPC= 0.66 (g/cm2)/sec (10 experiments), and stepwiseloading (38 experiments). The average RPC for stepwiseloading was 0.13 (g/cm2)/sec. At smaller RPC, the curvesof constant pressure are not as steep as at a larger RPC.This indicates that the diameter of the esophagus at a givenpressure and at smaller RPC is very readily influenced bysmall changes in the RPC.

consequence the area of the hysteresis loop progressivelydecreases in all experimental situations, and eventuallybecomes constant as a stable hysteresis loop (2) isreached and successive loading-unloading cycles followthe same path.

The number of cycles required to reach a stable hys-teresis loop varies with the type of material, the RPC,and the maximum load reached. Thus for the mucosa (Pm..= 80 g/cm2, RPC= 0.66 (g/cm2)/sec), the stable hys-teresis loop is reached in the second cycle and the thirdloading-unloading cycle is just superimposed on the sec-ond one. On the other hand, for the esophagus at thesame Pmas and RPC, the stable loop is not reached evenafter six cycles.

Residual deformation. The outer diameter of theesophagus at the end of a loading and unloading cyclewas different from the initial diameter at the onset ofthe cycle. The change in diameter of the esophagus fromits initial diameter, after it has undergone a loadingcycle, is the residual deformation. Like the area of thehysteresis loop, the residual deformation was dependentupon the rate of pressure change, maximum pressure

Mechanical Properties of the Esophageal Wall 1459

2Pg/cm2

640I IJ~~~~~~~~~~~~~~/ill

(A) , Ill;.480 successive

loading curves I 1"RPC=5

320 ESOPHAGUS , SIl

i60 7 4

. ,' /111~~~~~~~~~~~~~~~o

2 3 4 Dmm

.640

A80

9*#

'II

(B) of,successive ijunloading IIcurves IIIRPC=5 N,

lili

11/1Ail

.11 /1,,

.320

.160

2 3 4

FIGURE 6 Successive loading (A) and unloading (B) curves for the esophagus at RPC= 5(g/cm2) /sec, Pmax = 640. (Mean of 10 experiments.) With each new cycle loading curvesshift to the right, producing an increase in diameter. The shift is larger at low pressure, andfor the first cycle. The unloading curves also show a similar shift to the right but the shiftwith successive cycles is much smaller.

reached, the type of the material, and ticycles applied. When adaptation has occurhysteresis loop the residual diameter also bThe amount of change in diameter betwcessive cycles becomes progressively sm;

. Pg/cm2

80

60

40

.20

SulozRFESOPHAGUS of/

, 1XJ,/St

* ,/ / /11

.1/ , // ,

f~~~~~t, 0,o/r1. O_ p

2 3

FIGURE 7 Successive loading curves of theRPC= 0.66 (g/cm2)/sec, Pmax = 80 g/cm2.experiments.) Note that the sigmoid behavictwo cycles disappears on subsequent four cyclnew cycle the curve shifts to the right.

ie number of disappears (Fig. 9). The total residual deformation,rred with the which is the sum of the residual deformations occurringecomes fixed. in each cycle, increases sharply at first, then slowly,een two suc- and finally becomes fixed, as the stable residual defor-aller until it mation. The stable residual deformation was reached af-

ter two cycles for the mucosa (RPC = 0.66 (g/cm2)/sec, Pmax = 80 g/cm') but was not reached for theesophagus at the same RPC and Pma.. At RPC= 5(g/cm2)/sec and Pmaz = 640 g/cm2, the stable residualdeformation was almost reached after five cycles.

iccessive The residual change in the diameter of the esophagusading curves after just one cycle was influenced by the rate of pres-'C =0.66 sure change and the maximum pressure reached. The

residual deformation was most marked for P..x = 640g/cm' and RPC= 5 (g/cm')/sec, least for the stepwiseloading, and intermediate for Pmax = 80 g/cm' andRPC= 0.66 (g/cm')/sec. The residual deformation formucosa alone was smaller than for the whole esophagusat comparable RPCand Pmax.

Time-dependent deformation (creep). The influenceof creep was studied in 10 rats. A pressure of 80 g/cm2was suddenly applied and kept for 15 min. The diameter

4 DaflWm1 was measured before application of the load and againesophagus at every minute thereafter. The diameter without load was

(Mean of 10 1.73 mm (SD ±0.15). There was a large increase inr in the first diameter in the 1st min of application of the load and[es. With each

after 1 min, the diameter was 3.71 mm(SD ±+0.27). Af-

1460 R. K. Goyal, P. Biancani, A. Phillips, and H. M. Spiro

Epg/cm2

ter 15 min the diameter was 3.84 mm(SD ±0.27) (Fig.10). This indicates that most of the deformation occursduring the 1st min after application of the load.

Three possible factors could influence this: (a) re-laxation in the muscle, (b) progressive realignment ofthe collagen fibers and microfibrils present (13), withresulting viscous resistance by the ground substance;and (c) relaxation inside the microfibrils themselves(8).

For primary tendon bundles in which the collagenfibrils are aligned in a very orderly fashion, it has beenfound (8) that creep is small. This leads us to believethat the larger part of the deformation which happensin the 1st min might be due to muscle relaxation as wellas to realignment and reorientation of collagen fibers.

Failure strength of the esophagus and of the mucosa.The contribution of the mucosa to the failure strengthof the esophagus was estimated by comparing the fail-ure pressure of the esophagus with that of the mucosaalone. To test the mucosa alone the muscular layer wascarefully dissected away in five rats and the mucosa wasleft in place. A rate of pressure increase (RPI) of 200(g/cm')/sec was applied. At this rate the failure pres-sure for the intact esophagus was 1190 g/cm2 (SD +78)and the mean failure diameter was 5.08 mm(SD +0.14).At the same RPI, the mean (+SD) failure pressure andfailure diameter for the mucosa alone were 694 (±+53)g/cm2 and 4.69 (±0.19) mmrespectively.

The failure pressure of the mucosa alone was 55% ofthe whole esophagus at the same RPI. However, as thefailure pressure of muscle layer could not be separatelytested with our technique, the precise contribution of themucosa to the failure pressure of the whole esophaguscannot be defined with certainty.

Failure strength and rate of loading. The dependenceof the failure pressure and failure diameter of the

lpg/crn

80

.60

.40

20

Ist cycleo loadng* unloading2nd and 3rd

MUCOSA 9 ? cyclea, o loading

,, 0 unloacingojf -NMtt

' ; I R PC=066

i34 mA/ jo

2 3 4 Dmm

Res. deform. mm

.2

/L.1

/l

C max = 640o Pmax = 80o mucosa

- residual deform.produced bysingle cycles

_-~ _ --total residual_- ~ deformation

5 6 No of cydes

FIGURE 9 Factors influencing the residual and total defor-mation. The residual deformation of the esophagus is largerat RPC=5 (g/cm2) /sec and Pmax = 640 g/cm' (A) thanat RPC= 0.66 (g/cm2)/sec and Pmax = 80 g/cm2 (B). Themucosa (C), when compared to the whole esophagus at thesame RPC= 0.66 (g/cm2)/sec and Pma. = 80 g/cm2, showsless residual deformation. With each successive cycle theresidual deformation (i.e. the difference in diameter at theend of two successive cycles) progressively decreases forall the experiments till it tends to reach zero. Stable residualdeformation (zero level) is reached very soon (thirdcycle) for the mucosa. For the esophagus, five cycles arerequired at RPC= 5 (g/cm')/sec and Pmas = 640 (g/cm')(A) and more than six at RPC= 0.66 (g/cm2)/sec andPmax = 80 (g/cm2) (B). (Each point represents mean ofseveral experiments.)

esophagus on the rate of loading was tested by com-paring the failure pressure and diameter of the intactesophagus at different rates of pressure increases. Fivespecimens were tested at RPI = 200 (g/cm2)/sec, andfive at RPI = c (g/cm')/sec.

The failure pressure was markedly influenced by therate of pressure increase, being significantly lower for

D,mm ~~~~~~~~SD13.

CREEPTESTP = 80g /cm2

1.7

5 10 15 min.

FIGURE 8 Successive loading-unloading cycles for the mu-cosa at RPC= 0.66 (g/cm')/sec, and Pm.. = 80 g/cm'.(Mean of 10 experiments.) The curves in the second cycleare different from those in the first cycle. The third cyclehas the same curves as the second, indicating that a stablehysteresis loop has been reached.

FIGURE 10 Time dependent deformation. After measuringthe resting diameter of the esophagus, a pressure of 80(g/cm') was suddenly applied. The diameter more thandoubled in the first minute and then only a small changeoccurred in the next 14 min. Each dot represents the meanof 10 experiments.

Mechanical Properties of the Esophageal Wall 1461

P, g/cm2

FIGURE 11 Contribution of muscular and mucosal layers tothe strength of the esophagus at low pressures. The pres-sure-diameter curve for the muscle layer has been calculatedby taking the difference between the mean curves for theesophagus (as a function of the inner diameter of this musclelayer which is given by Inner diameter = Outer diameter-2 X thickness) and the mucosa alone (as a function ofouter diameter of the mucosa, which would be equal to theinner diameter of the muscle layer when the mucosa isfully distended). For pressures less than 40 g/cm2 the con-tribution of the mucosa is less than 1 g/cm'.

an RPI of 5 (g/cm2)/sec (P = 864 ±131 g/cm2), thanfor RPI = 200 (g/cm2)/sec (P = 1190 +78 g/cm2).The change in failure pressure is not surprising. Byreducing the RPI the contribution of the viscous ele-ment is reduced. At RPI = 200 (g/cm')/sec the failureis reached in 6 sec, while at RPI = 5 (g/cm2)/sec ittakes 172 sec. In this longer time some stress relaxa-tion takes place, thus reducing the final failure pressure.

The failure diameter was also influenced by the RPIbut the failure diameter was larger for higher RPI.The failure diameter was 4.77 (±0.30) mmfor RPI =5 (g/cm')/sec, and 5.08 (±0.14) mmfor RPI = 200(g/cm')/sec.

DISCUSSIONThe esophagus in experimental animals or in man isdesigned to perform two basic functions; namely, "hold-ing" and "propelling." With respect to the first function,the esophagus behaves like an inert pipe, the purposeof which is to contain materials as they travel throughit either from the mouth to the stomach, as duringswallowing, or backwards, as during vomiting. Thepropelling force in the esophagus is provided by a wave-like muscular contraction or peristalsis. The chief con-cern of this investigation was to study the "holding"function of this organ and to evaluate its response tovarious types of intraluminal pressures.

In general, the pressure diameter relationship of theesophagus was exponential. This behavior is, obviously,due to both the mucosa and the muscle coat which inturn depends on the behavior of individual componentslike the epithelial cells, the connective tissue, and themuscle fibers and their interaction with each other.

The structural organization of the esophageal wallcontributes to nonlinear stress-strain relationship. Withsmall deformation the mucosa does not contribute to thestrength of the wall, but it just unfolds or takes verylittle load until the outer mucosal diameter reaches2.40 mm, which corresponds to an outer esophageal di-ameter 2.65 mm(Fig. 11). This finding has some sig-nificance. It shows that mucosal disease by itself doesnot influence the diameter of the esophagus at smallloads such as might be imposed by a bolus of food.However, with muscle involvement, as in scleroderma,significant changes in the diameter of the esophagusmay occur.

Data on the stress-strain relationship of epithelialcells are scanty, but nonlinear stress-strain relationshiphas been shown to exist for connective tissues and themuscle fibers. In the collagen tissue, such a relationshiphas been attributed to a recruitment model (8, 9, 13)which can be explained in the following way: collagenfibers in the unstretched state form wavy patterns andare more or less disorganized in orientation, dependingon the function of the organ in which they are located.With increasing deformation an increasing number offibers straighten and start bearing load (8, 9). More-over, with increasing loads, realignment may occurwithin the single collagen fibers, as the microfibrilsstraighten and realign in their turn. Other fibers, likeelastic and reticular, also become reoriented with in-creasing loads.

Thus the stiffness of connective tissues increases withthe load, producing an exponential stress-strain relation-ship. Interestingly, however, the exponential stress-strain relationship appears not only for composite con-nective tissues, where architectural rearrangements con-tribute to it, but also for the single fibrils. Tests runon single elastic fibrils (14) show that a single fibril,teased out of the bundle which contains it, still showsincreasing stiffness with increasing load.

Nonexcited muscles also behave in a similar way.The stress-strain relationship of "passive" muscles isexponential in character (5, 6), which could probablybe explained by the presence of connective tissue sheathsaround the muscle fibers.

Hill (15) reported that for relaxed muscles the loga-rithm of the tension was proportional to the length ofthe stretched muscle. In 1967, Fung (16) found thisalso to be true for the mesenteric membrane of therabbit. In 1969, Stromberg and Wiederhielm (8) found

1462 R. K. Goyal, P. Biancani, A. Phillips, and H. M. Spiro

that rat tendons and other connective tissues have thesame property.

In mathematical terms this property can be de-scribed by

dT= KT (1)

where stress

and strain

and

P X DoT=-

2 to

2 (Do)

P = intraluminal pressureDo = initial diameter D

to = initial thickness

This equation is satisfied by

T = GeKE (2)

In this equation, however, when E = 0, T $ 0,but at zero strain the stress should also be zero.

In order to have T = 0 at E = 0, we will modifyequation (1) and write

dTdE=KT+H (3)

which is satisfied by

T= GeKE-G (4)

where H = KGis the slope of the curve at E = 0.

Thus the one-dimensional stress-strain relationshipof many soft biological tissues, if the hysteresis loop isneglected, is described to some approximation by twoconstants, K and G.

Stromberg and Wiederhielm (8) showed that K(Fung's modulus) decreases with decreasing degrees oforganization of the tissues. The constant K is 450 forprimary tendon bundles in rat and is 12 for rabbitmesentery. Mesentery is a typical example of loose con-nective tissue constituted by a randomly oriented, two-dimensional network, while primary tendon bundles are

highly organized. In the rat's esophagus K = 2.3, G=

5 for the whole esophagus under stepwise loading, andK= 3.6, G= 0.0052 for the mucosa alone under con-stant RPI. In general G is very small for tissues thatundergo a large deformation before a small increasein stress appears, as is the case of the mucosa. The cal-culated stress-strain curves for the esophagus and mucosaare very close to the curves obtained experimentally dur-ing loading (Fig. 12, A, B), and thus would give anaccurate representation of the behavior of the esophagusif it were perfectly elastic. However, the loading curvesof the esophagus and the mucosa alone, are differentfrom the unloading curves in all experiments. The un-loading curve is always to the right of the loading curve,forming a loop (hysteresis loop). The area of the hys-teresis loop, which is enclosed by a loading and the suc-cessive unloading curve, is directly proportional to thework dissipated in the loading-unloading cycle. Thearea of the hysteresis loop depends on the history of

T,g/crr?

600 b experimental* cakaUjated 9

T=5 xe23E-5 i

P400 E

f

(A) ESOPHAGUS i

200 i/fy

Of

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Tg/cm2

3000 o exp* cala

T=0.05

2000

(B) MUCO'

1000

ueri imentalulated ?,2xe3.6E 0052 '

Il

II

f

I,

-

Iit

,P,-l/

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FIGURE 12 Comparison of the experimentally determined stress-strain relationshipwith the values calculated from the equation. T = G X eE- G For the Esophagusunder Stepwise Loading. For the whole esophagus G= 5; K = 2.3 and for the mucosaG= 0.052; K = 3.6. Note the close agreement between the experimental and thecalculated curves. The experimental curves are mean of 10 experiments.

Mechanical Properties of the Esophageal Wall 1463

loading. This dependence is different for the esophagusand for the mucosa alone.

For the mucosa, at RPC= 0.66 (g/cm2)/sec andPraz = 80 g/cm2, the hysteresis loop after the secondcycle repeats the same paths (stable hysteresis loop).Whereas, for the whole esophagus, the stable hysteresisloop is not reached before six or more loading andunloading cycles. The reduction in the hysteresis loopfrom one cycle to another is mainly due to the changeof the loading curve, while the unloading curve showsonly little change. The appearance of the stable hystere-sis loop was first described by Remington in 1955 (2)and has been called adaptation by some (4).

The shift between the first and second hysteresis loopis probably due to deformations and rearrangementsoccurring during the first cycle, and depends on themaximum load applied. The stable hysteresis loop ap-pears to be due to energy dissipated during loadingand unloading, as the connective tissue fibers changetheir orientation within the viscous ground substance.When the fibers are all parallel, as in tendons, the stablehysteresis loop is very small.

Fukaya, Martin, Young, and Katsura (4) observedthat changing to higher tension requires new adaptation.They thought that the rearrangement which resulted inrepeated pathways for a given maximum load is dis-turbed when the maximum load is increased. and re-peated cycling is necessary to establish a new rearrange-ment compatible with the new peak load.

The difference in behavior between the whole esopha-gus and the mucosa alone can be attributed to thepresence of the muscular layer (muscularis externa).The loading curves for the muscular layer are not ex-ponential, but exhibit sigmoid behavior in the first twocycles. After the first two cycles the sigmoid behaviordisappears and the curves become exponential in shape.The reason for such behavior is not entirely clear.Tetanized muscles (muscles under sustained state ofcontraction) have been shown (6) to exhibit sigmoidstress-strain relationship, the sigmoid bump being re-lated to the contractile activity of the muscle. The sig-moid curve is also given by the superimposition of thecurve of "active" tension, and the curve of "passive"tension. The curve of "passive" tension, that is, thestress-strain curve of a "passive" muscle, is exponen-tial in shape. Muscular fibers can exert active tensionuntil they have been shortened to a minimum length, Li.When such a minimum length is reached, the musclecannot contract any further and the active tension de-creases to zero. Also muscular fibers lose their abilityto contract if they are stretched above a certain maxi-mum length, L2. For some length, Lo (comprised be-tween L1 and L2) the muscles can exert their maximum

active tension (5, 6). These observations suggest thepresence of a phenomenon similar to what has beendescribed as Starling's law of the heart (17).

The superposition of the exponential "passive" curve

and of the parabolic "active" curve gives a sigmoidcurve of total tension for muscular fibers which is simi-lar to that found for loading in the first cycle. It is pos-sible that the sigmoid behavior may be due to themuscles maintaining themselves in a state of partialcontraction or tone. However, the fact that the sigmoidpattern gives way to an exponential pressure-diameterrelationship with repeated cycles suggests that the "ac-tive tone" of the muscle is not continuously present andrepeatedly exhibited. This would explain the presence ofsigmoid stress-strain relationship of the muscle in thefirst cycle and its disappearance in subsequent ones.

When pressure is applied, the contraction is gradu-ally destroyed by viscous deformation as the test goeson. Thus at low tension the muscles act like inert vis-cous elements. This explains why the behavior of themucosa with a constant RPC is so similar to that of theesophagus under stepwise loading (Fig. 4). The step-wise loading, where a certain time passes between suc-

cessive increases in load, gives the muscles time to relax(18, 19), until their contribution disappears, and theentire esophagus behaves like the mucosa.

In most experiments described in literature (2-9, 14,16, 18-21), tissues were removed from the body andmounted on a testing device. Although the effect of cut-

ting an artery on its elasticity is small (22), many bio-logical tissues are very soft and undergo large deforma-tions when comparatively small forces are applied. Forthis reason it is difficult to measure the resting or un-

disturbed dimensions after the tissues are removed fromthe body. Moreover, the mechanical properties of bio-logical tissues depend on the history of loading. If some

biological tissues are stretched and then released, theirbehavior upon successive stretching will be affected bythe rate of application and the magnitude of the previ-ous load. Thus the effect of removing the tissues fromthe body and of installing them in the testing devicebecomes hard to estimate and eliminate since it is veryeasy to produce large deformations during these proc-esses. For these reasons, we feel that the in situ tech-nique is desirable in the investigation of mechanicalbehavior of biological tissues.

The results of the experiments on the failure pressureindicate that the mucosa may make important contribu-tions to the strength of the esophageal wall at the failurepressure. This is consistent with the observation thatthe mucosal inflammation is an important factor inthe production of esophageal rupture (23).

1464 R. K. Goyal, P. Biancani, A. Phillips, and H. M. Spiro

FIGURE 13 Three parameter solid.

These studies further show that the failure pressureis influenced by not only the maximum pressure reachedbut also the rate of pressure increase. Moreover, thediameter at which rupture occurs is also modified bythe rate of pressure increase. The failure diameter islarger with a higher RPI. This phenomenon can beexplained by a model of spring and dashpot (Fig. 13).If a viscoelastic element (Kelvin solid) is in serieswith an elastic element (20, 21), one could say that athigher pressures associated with larger RPI, the serieselastic element deforms more than the viscoelastic ele-ment. If the increase of deformation of the series elasticelement is larger, because of higher load, than thedecrease in deformation of the viscous element due tohigher rate, then the breaking diameter would be largerat a larger RPI.

In conclusion, this study describes a technique forinvestigation of the mechanical properties of the esopha-gus in situ, which is desirable because the mechanicalbehavior is modified by inadvertent load applicationswhen in vitro studies are performed. Because the over-all organization of the walls of various segments ofgastrointestinal tract is closely similar, it appears thatthey will show similar qualitative responses. A simpleequation has been given for representation of the elasticbehavior of this material. The data provide some ex-perimental background for constructing constitutiveequations for the walls of the gastrointestinal tract.

ACKNOWLEDGMENTSThe authors wish to thank Dr. Paul Schwartz for his help-ful suggestions.

This research was supported in part by the Rose BrothersFund at Yale University, and in part by the American Ma-chine and Foundry Foundation.

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Mechanical Properties of the Esophageal Wall 1465